Place first 3 ingredients in a large microwave-safe bowl. Cover tightly with plastic wrap, folding back a small edge to allow steam to escape. Microwave at HIGH 8 minutes or until squash is tender; drain. Sprinkle with salt and pepper.
Drain tomatoes well, pressing between paper towels. Stir together tomatoes, chicken, and next 4 ingredients. Layer one-third each soup mixture, squash mixture, breadcrumbs, and Cheddar cheese in a lightly greased 6-qt. slow cooker. Repeat layers twice. Top with Parmesan cheese.
Cover and cook on HIGH 4 hours or until bubbly and edges are golden. Uncover and cook on HIGH 30 minutes. Let stand 10 minutes before serving.
This is tasty, my husband loved it, my little kids didn't, I liked it. If you use all the squash and zucchini there is a lot of liquid--my son thought it was soup. It isn't pretty but smells wonderful. I think you should toast the breadcrumbs for best effect. It filled up my 7 quart slowcooker to the top, and it makes a ton of food. It serves more than six.